Question

leo drew a line that is perpendicular to the line shown on the grid and passes through point (f, g). which of the following is the equation of leos line?
options:
$y - f = -\frac{1}{3}(x - g)$
$y - g = -\frac{1}{3}(x - f)$
$y - g = -3(x - f)$
$y - f = -3(x - g)$

question 11
(multiple choice worth 1 points)
(04.01hr mc)
sammy is classifying quadrilateral efgh. how can she use coordinate geometry to determine whether efgh is a rectangle?
e(7, 10), f(4, 7), g(6, 5), h(9, 8)
options:
sammy can use the distance formula to show opposite sides are equal and the slope formula to show that consecutive sides have opposite reciprocal slopes.
sammy can use the distance formula to show opposite are perpendicular and the slope formula to show that consecutive sides are equal
sammy can use the distance formula to show that all sides are equal and the slope formula to show that consecutive sides have the same slope
sammy can use the distance formula to show that all sides are parallel and the slope formula to show that consecutive sides are equal

Explanation:

---

First Question

Step1: Find slope of given line

Using two points on the line, e.g., $(0,-2)$ and $(1,1)$:
$\text{slope} = \frac{1 - (-2)}{1 - 0} = 3$

Step2: Find perpendicular slope

Perpendicular slopes are negative reciprocals:
$\text{perpendicular slope} = -\frac{1}{3}$

Step3: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$, where $(x_1,y_1)=(F,G)$:
$y - G = -\frac{1}{3}(x - F)$

A rectangle is defined as a quadrilateral with opposite sides equal in length, and consecutive sides that are perpendicular (their slopes are negative reciprocals). The distance formula verifies side lengths, and the slope formula verifies perpendicularity of adjacent sides.

Answer:

$\boldsymbol{y - G = -\frac{1}{3}(x - F)}$

---

Second Question